Dunkl-Schrödinger operators

DOI10.1007/s11785-018-0834-1zbMath1480.47056arXiv1802.01547OpenAlexW2786022511MaRDI QIDQ2313012

Amel Hammi, Bechir Amri

Publication date: 18 July 2019

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01547

zbMATH Keywords

Schrödinger operatorself-adjoint operatorDunkl operators

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Schrödinger operator, Schrödinger equation (35J10) Other transforms and operators of Fourier type (43A32) Operators arising in mathematical physics (47B93)

Related Items

Singular integrals in the rational Dunkl setting, Spectral decomposition of Dunkl Laplacian and application to a radial integral representation for the Dunkl kernel, Restriction theorem for the Fourier-Dunkl transform. I: Cone surface, On the path integral formulation of Wigner–Dunkl quantum mechanics, Restriction theorem for the Fourier-Dunkl transform and its applications to Strichartz inequalities, Remarks on Dunkl translations of non-radial kernels, Semigroup and Riesz transform for the Dunkl-Schrödinger operators, Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces, On semigroups generated by sums of even powers of Dunkl operators, Behavior of eigenvalues of certain Schrödinger operators in the rational Dunkl setting, Harmonic functions, conjugate harmonic functions and the Hardy space \(H^1\) in the rational Dunkl setting, Upper and lower bounds for the Dunkl heat kernel, Upper and lower bounds for Littlewood–Paley square functions in the Dunkl setting, The dual of the Hardy space associated with the Dunkl operators

Cites Work

• Riesz transforms for Dunkl Hermite expansions
• Dunkl spectral multipliers with values in UMD lattices
• \(BMO_L(\mathbb H^n)\) spaces and Carleson measures for Schrödinger operators
• Riesz transforms for the dunkl harmonic oscillator
• Singular integral operators with non-smooth kernels on irregular domains
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• \(L^p\) estimates of Schrödinger operators on nilpotent groups
• The Dunkl transform
• Convolution operator and maximal function for the Dunkl transform
• The functional calculus for sectorial operators
• Semigroup kernels, Poisson bounds, and holomorphic functional calculus
• The \(L^p\)-continuity of imaginary powers of the Dunkl harmonic oscillator
• Lp boundedness of Riesz transform related to Schroedinger operators on a manifold
• Differential-Difference Operators Associated to Reflection Groups
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item